Answer :
Let's analyze the given information step-by-step based on the notation [tex]\[ _{90}^{234}\text{Th} \][/tex]:
1. Atomic Number (Z):
- The atomic number is the number written as the subscript in the notation [tex]\[ _{90}^{234}\text{Th} \][/tex].
- This number represents the number of protons in the nucleus.
- Here, the atomic number (Z) is 90.
2. Mass Number (A):
- The mass number is the number written as the superscript in the notation [tex]\[ _{90}^{234}\text{Th} \][/tex].
- This number represents the total number of protons and neutrons in the nucleus.
- Here, the mass number (A) is 234.
3. Number of Neutrons:
- The number of neutrons (N) can be calculated using the formula:
[tex]\[ N = A - Z \][/tex]
- Substituting the values:
[tex]\[ N = 234 - 90 = 144 \][/tex]
- So, the number of neutrons is 144.
4. Number of Protons:
- The number of protons is equal to the atomic number, which we already identified as 90.
Now, let's go through the given statements one by one:
1. The atomic number of the radioactive nuclide is 90.
- This statement is correct because the atomic number is indeed 90.
2. The mass number of the radioactive nuclide is 144.
- This statement is incorrect. The mass number is 234, not 144. The value 144 corresponds to the number of neutrons, not the mass number.
3. The number of neutrons that are present in the nucleus of each atom is 324.
- This statement is incorrect. The number of neutrons is 144, not 324.
4. The number of protons that are present in the nucleus of each atom is 234.
- This statement is incorrect. The number of protons is 90, not 234. The value 234 corresponds to the mass number, not the number of protons.
In conclusion, the correct statement among the options given is:
The atomic number of the radioactive nuclide is 90.
1. Atomic Number (Z):
- The atomic number is the number written as the subscript in the notation [tex]\[ _{90}^{234}\text{Th} \][/tex].
- This number represents the number of protons in the nucleus.
- Here, the atomic number (Z) is 90.
2. Mass Number (A):
- The mass number is the number written as the superscript in the notation [tex]\[ _{90}^{234}\text{Th} \][/tex].
- This number represents the total number of protons and neutrons in the nucleus.
- Here, the mass number (A) is 234.
3. Number of Neutrons:
- The number of neutrons (N) can be calculated using the formula:
[tex]\[ N = A - Z \][/tex]
- Substituting the values:
[tex]\[ N = 234 - 90 = 144 \][/tex]
- So, the number of neutrons is 144.
4. Number of Protons:
- The number of protons is equal to the atomic number, which we already identified as 90.
Now, let's go through the given statements one by one:
1. The atomic number of the radioactive nuclide is 90.
- This statement is correct because the atomic number is indeed 90.
2. The mass number of the radioactive nuclide is 144.
- This statement is incorrect. The mass number is 234, not 144. The value 144 corresponds to the number of neutrons, not the mass number.
3. The number of neutrons that are present in the nucleus of each atom is 324.
- This statement is incorrect. The number of neutrons is 144, not 324.
4. The number of protons that are present in the nucleus of each atom is 234.
- This statement is incorrect. The number of protons is 90, not 234. The value 234 corresponds to the mass number, not the number of protons.
In conclusion, the correct statement among the options given is:
The atomic number of the radioactive nuclide is 90.
